Changing
variables to u and v where u = A + B and v = A – B,
i.e. substituting A = (u + v)/2 and B =
(u – v)/2 :
(u + v)^{2}/4 + (u – v)^{2}/4
= 7 which gives u^{2} + v^{2} = 14 (1)
& (u + v)^{3}/8 + (u – v)^{3}/8 = 10 which gives
u(u^{2} + 3v^{2}) = 40
(2)
From (1), v^{2} = 14 – u^{2}, which can now be substituted into
(2):
u(u^{2} + 42 – 3u^{2})
= 40
u^{3} 21u + 20 = 0
(u – 1)(u – 4)(u + 5) = 0 giving a
+ b = u = 1, 4, 5
Was I alone in wondering whether ‘maximum real value of a + b’
was meant to be ‘maximum real part of a + b’? All is well, it turns
out that a + b can only have real values, and the maximum is 4.

Posted by Harry
on 20151212 15:48:36 